1. Field of Invention
The present invention relates generally to phase interferometric antenna systems that measure the direction of the received signal and, more specifically, to methods for resolving phase ambiguities in phase interferometers that provide direction finding capabilities over a wide field of view and bandwidth.
2. Description of the Related Art
Interferometric systems measure the direction of arrival of signals received by the antenna elements comprising the interferometer. The interferometer antenna system consists of an array of antenna elements separated by known distances. These distances are commonly referred to as baselines. In operation, the phase difference of the signals received by the antenna elements is measured and used to establish the signal arrival direction. For example, if the antenna elements are located on a planar surface and if the signal arrives normal to the surface, then signal outputs of each antenna element are in phase, and the relative phase difference between the elements is ideally zero. If the signal arrives obliquely to the plane, the phase differences between the elements vary dependent on the signal frequency, the baseline values and signal direction. The arrival direction of the signal is then derived based on the phase difference values between the antenna elements comprising the interferometer.
A problem arises, however, because the phase between the elements can only be measured over a 360xc2x0 range. When the baseline dimension exceeds one half of the wavelength of the incident signal, the phase difference between antenna elements can span more than 360 degrees. Consequently, more than one possible signal arrival direction can be obtained, and these multiple arrival directions are commonly referred to as ambiguities. What is needed is a way to determine the proper ambiguity so that the direction of the signal can be uniquely and correctly determined.
In practice, the design of an interferometric system must satisfy three requirements. First, the antenna elements must have sufficient sensitivity to detect the signals of interest. Second, the angular accuracy depends on the maximum baseline dimension and the accuracy with which the phase difference values can be measured. Third, the design must be able to detect and locate signals over a required field of view and a required frequency range.
These three requirements have some apparent conflicts. The antenna element size must be sufficiently large to receive an adequate signal level. The physical size of the element derived from the sensitivity requirement limits the separation between elements because the elements cannot physically overlap. Thus, a lower bound exists on element spacing. When the antenna element size exceeds one half wavelength, ambiguities exist even when the elements are touching. The overall baseline dimension is determined from the angular accuracy requirement, required field of view and frequency of operation, and the phase measurement accuracy. Increasing the baseline dimension, i.e., the overall separation between elements, increases the angular accuracy of the solution and the number of phase ambiguities but reduces the spacing between ambiguities. The ability to meet the field of view requirement results from having antenna elements that achieve the required sensitivity over the field of view; but the broad antenna coverage conflicts with high antenna gain levels that may be needed for sensitivity requirements. Thus, the design of practical interferometers requires examination of these requirements and resolution of the conflicts between them.
Interferometers are configured for a variety of applications, and consequently have differing approaches to the problem posed by the ambiguities. Interferometers with narrow field of view requirements and relatively high gain levels (to meet sensitivity requirements) typically use aperture antennas that can also provide monopulse-processing capabilities. Monopulse processing uses two types of antenna patterns produced in the same aperture, a sum beam and a difference beam. The sum beam provides the signal reception, and the combined processing of the sum and difference beams provides a coarse estimate of the signal direction. The coarse estimate of the signal arrival direction is obtained from the ratio of the signals received by the difference and sum beams and its sign. To first order, the ratio of the difference signal and the sum signal linearly increases as the signal arrival direction moves away from the antenna""s axis. The sign of this ratio changes depending on which side of the antenna""s axis corresponds to the signal arrival direction. For example, the sign can be positive for signals arriving to the left of the antenna""s axis and negative for signals arriving to the right of the antenna""s axis. Thus, by measuring the ratio of the difference and sum signals and the sign of this ratio, a coarse estimate of the signal arrival direction can be determined.
When the above method is applied to narrow field of view interferometers, the interferometric elements have a monopulse processing capability. The coarse estimate of the signal arrival direction derived from the monopulse processing of the interferometric element is used to resolve the correct signal arrival direction from the possible interferometric ambiguities. The overall accuracy of the signal arrival direction is achieved from the interferometric processing and is significantly better than the accuracy provided by the monopulse processing of the interferometric elements. Thus, the overall angular accuracy of the system depends on the interferometric measurement, and the monopulse processing identifies the correct signal arrival direction from the possible ambiguities of the interferometer.
In practice, if the baseline of the interferometer is about five times the diameter of the elements, the ambiguities can be resolved with high confidence. The overall angular accuracy of such an interferometer is about ten times better than the monopulse estimate provided by the interferometric antenna element. One advantage of this method is that the ambiguity resolution is not frequency dependent so that the system can be used to locate signals over a very wide bandwidth. Frequency increases also improve the accuracy of the monopulse estimate of signal arrival, offsetting the reduction in the angular separation between phase ambiguities. Similarly, frequency decreases reduce the accuracy of the monopulse estimate of the signal arrival, offsetting the increase in the angular separation between phase ambiguities. Thus, the ability to resolve phase ambiguities by monopulse processing persists over a very broad bandwidth. Similar frequency independent operation is desired for interferometers for wide field of view applications.
Another method to resolve interferometric ambiguities is commonly used by the radio astronomy community. In this application, the antenna elements are widely separated and have a very large number of ambiguities. However, the required sensitivity for this application requires very long time periods to integrate the signal for detection. During this long integration period, the earth rotates, and this rotation of the earth provides the ambiguity resolution. This method cannot be used without motion between the interferometer and the signal and when the signal arrival direction must be determined in a timely fashion.
Yet another method applies to the case where a wide field of view is required. In this case, the interferometric elements have a broad pattern to meet the field of view requirements and are small and relatively inexpensive. A common approach to ambiguity resolution uses multiple elements within the overall baseline. These additional elements and their smaller baseline values have a reduced number of ambiguities. The minimum spacing between elements is limited to the size of the elements and this baseline has the minimum number of ambiguities. In fact, if this separation is less than one-half wavelength, no phase ambiguities can occur.
The above method, however, has several shortcomings. The system complexity and expense grow with the number of elements. The element size may be sufficient to physically preclude a one-half wavelength spacing between elements. If the system is required to operate over wide bandwidths, then the ambiguity resolution problem is more complex because the number of ambiguities and the combination of baseline values for ambiguity resolution increase. The physical size of these elements can exceed the one-half wavelength separation that produces ambiguity-free operation particularly when broad bandwidth operation is required. Wide bandwidth systems often use frequency independent antenna elements such as spiral antennas or log periodic antennas. While such elements can incorporate monopulse processing, the accuracy of the monopulse elements does not vary with frequency because the broad antenna coverage is also frequency independent. Thus, the previously cited method of using monopulse processing to resolve phase ambiguities does not work over wide bandwidths with broad coverage, frequency independent antennas.
A method for reliably and correctly resolving phase ambiguities with minimum system complexity is needed for applications having wide field of view, high angular accuracy and wide bandwidth requirements. A method for selecting baseline dimensions in such a way as to minimize the required number of interferometric elements is needed. An ambiguity resolution methodology that is not limited by the physical constraints dictated by the element dimensions is also needed.
The present invention pertains to wide field of view interferometric systems that have high angular accuracy and require operation over wide bandwidths. In such designs, the individual interferometric elements have wide fields of view and consequently are relatively small. Multiple elements within the overall baseline provide a means to resolve the interferometric ambiguities, and have baseline dimensions that are smaller than the overall baseline value. According to a preferred embodiment of the present invention, a method is provided for selecting fractional baseline values and for synthetically obtaining additional baseline values without incurring the expense and complexity of additional interferometric elements. According to a preferred embodiment of the present invention, the number of interferometric elements is minimized while still providing reliable phase ambiguity resolution.
A method for resolving interferometric ambiguities according to an exemplary preferred embodiment of the present invention first involves determining the overall baseline dimension from the angular accuracy requirements of the interferometric system together with the achievable phase measurement accuracy. A baseline dimension for a secondary element to be located within the overall baseline is selected to produce ambiguities that coincide with a limited number of the ambiguities of the overall baseline. This condition is achieved by using secondary elements in locations that are integer fractions of the overall baseline dimension. Thus, the overall baseline equals 4, 5, 6, etc. times the fractional baseline. The ambiguities of the overall baseline are more numerous than the ambiguities of the fractional baseline. The ambiguities of the two baselines that coincide represent possible signal directions. The ambiguities of the overall baseline that do not coincide with the ambiguities of the smaller fractional baseline can be eliminated as possible signal directions. The spacing between the ambiguities increases and decreases as the frequency of operation decreases and increases, respectively. Thus, this method for selecting baseline dimensions immediately reduces some ambiguities from consideration, and also provides a method that is frequency independent.
The fractional baseline value together with its phase measurement accuracy is selected to have sufficient angular accuracy to resolve the separation between the ambiguities of the overall baseline correctly and reliably. Like the overall baseline, the angular accuracy of the fractional baseline depends on the accuracy of measuring the phase difference between elements. This phase measurement accuracy is determined, in a preferred embodiment, by constructing an error budget composed of the individual error sources limiting phase measurement accuracy. These errors include the uncertainties caused by thermal noise sources, imperfections in the phase response of the elements and knowledge of their positions, bias errors resulting from insertion phase differences in the cabling, phase tracking limitations in receiver electronics, etc. If the statistics and confidence intervals of the phase measurement accuracy are known, a probability of correct ambiguity resolution can be derived and the integer fraction can be determined to meet these confidence values.
The reliable resolution of ambiguities requires the angular accuracy of the fractional baseline to be better than the angular separation between the ambiguities of the overall baseline. In many cases, however, the element size and bandwidth requirements preclude a separation that is less than one half wavelength. In other cases, the angular accuracy requirements are also accompanied by separations between ambiguities that are too small to be reliably resolved by a single additional baseline element.
According to an exemplary preferred embodiment of the present invention, if ambiguities persist, additional elements can be inserted within the baseline, and the process continued. Ultimately, the resulting fractional baseline is shorter than the minimum physical separation between interferometric elements that is dictated.
According to an exemplary preferred embodiment of the present invention, a synthetic baseline is obtained by arraying the two elements with the smallest separation. When two interferometric elements are combined, the phase center of the resulting array lies between the elements. The phase center location depends on the amplitude ratio of their combining and can be varied to produce different baseline values. For example, when the elements are equally combined, the phase center lies exactly between the two elements. The array pattern of the combined elements differs from the element pattern and is examined to insure that the array provides adequate gain over the design field of view. For broad coverage antennas used by wide field of view applications, the antenna elements are usually sufficiently small that the arrayed pattern is acceptable. The synthetic baseline of the present invention solves the shortcoming imposed by an inability to physically overlap interferometric elements.
In accordance with one embodiment of the present invention, a method for resolving interferometric ambiguities for an interferometer system with antenna elements which define an overall baseline includes the steps of: employing an angular accuracy requirement and an achievable phase measurement accuracy to determine an overall baseline dimension for the interferometer system; selecting a secondary element baseline dimension, for a secondary element to be located within the overall baseline, as an integer fraction of the overall baseline dimension, the secondary element and one of the antenna elements defining a fractional baseline, such that ambiguities produced by the fractional baseline coincide with a portion of ambiguities produced by the overall baseline; and eliminating from consideration as possible signal directions the ambiguities of the overall baseline that do not coincide with the ambiguities of the fractional baseline. In a preferred embodiment, the fractional baseline and a phase measurement accuracy of the fractional baseline are selected to provide sufficient angular accuracy to resolve separations between the ambiguities of the overall baseline. In a preferred embodiment, the phase measurement accuracy of the fractional baseline is determined by constructing an error budget composed of one or more error sources that limit phase measurement accuracy. The error sources include (but are not limited to) one or more of: uncertainties caused by thermal noise sources, imperfections in a phase response of the elements and knowledge of positions of the elements, bias errors resulting from insertion phase differences in cabling, and phase tracking limitations in receiver electronics. In a preferred embodiment, a probability of correct ambiguity resolution is derived from statistics and confidence intervals of the phase measurement accuracy, and the integer fraction is selected to meet the statistics and confidence intervals. In a preferred embodiment, the method further includes the step of locating additional elements within the overall baseline if ambiguities still persist.
In accordance with another embodiment of the present invention, a method for resolving interferometric ambiguities for an interferometer system with interferometric elements that define an overall baseline includes the steps of: employing an angular accuracy requirement and an achievable phase measurement accuracy to determine an overall baseline dimension for the interferometer system; and inserting one or more additional interferometric elements within the overall baseline such that baseline dimensions of the additional interferometric elements are integer fractions of the overall baseline dimension, the integer fractions being selected to provide ambiguity resolution that meets a required confidence value. In a preferred embodiment, the one or more additional interferometric elements comprise actual antenna elements. In a preferred embodiment, the step of inserting one or more additional interferometric elements includes creating a synthetic baseline by electronically combining the interferometric elements. In a preferred embodiment, the dimension of the synthetic baseline is smaller than dimensions of baselines limited by physical separations between the interferometric elements.
In accordance with another embodiment of the present invention, a method for resolving interferometric ambiguities for an interferometer system with antenna elements includes the steps of: combining two elements of the interferometric system such that the combined elements have a phase center; producing a synthetic baseline whose dimension is a separation between one of the combined elements and the phase center of the combined elements; and employing the synthetic baseline to resolve ambiguities that cannot be resolved by baselines between the antenna elements. In a preferred embodiment, the dimension of the synthetic baseline is smaller than a separation between the combined elements. In a preferred embodiment, the combined elements have a smaller separation than any two elements of the interferometric system. In a preferred embodiment, the combined elements are combined such that the synthetic baseline is one half the size of the baseline between the combined elements. In a preferred embodiment, the combined elements are combined with an unequal amplitude combination.
The above described and many other features and attendant advantages of the present invention will become apparent as the invention becomes better understood by reference to the following detailed description when considered in conjunction with the accompanying drawings.